is the de Broglie
thermal wavelength [1]},
and \(\mbox{Li}_\nu \) 
is the polylogarithmic function [2]}, [3]}.
The values of \(\mu >0\) , i.e., \(z>1\) , are forbidden
in the ideal Bose gas. The point
\(\mu =0\)  corresponds to an onset of the Bose-Einstein condensation in the system
of bosons. For fermions, any values of \(\mu \) 
are possible, i.e., integrals (REF ) and () exist for
\(\theta _i=-1\)  at all real values of \(\mu \) .
The power series
(REF ) and () are obviously convergent at
\(z < 1\) . For the Fermi statistics at \(z>1\) , the integral
representation of the corresponding polylogarithmic function
can be used.
Particularly,
at \(z\rightarrow \infty \)  one can use the asymptotic Sommerfeld expansion of the
\(\mbox{Li}_{\nu }(-z)\)  functions over \(1/\mbox{ln}^2|z|\) 
[4]}.
